If $\left|\frac{x^2+kx+1}{x^2+x+1}\right| < 3$ for all real $x$,then $k$ is in the interval

Let $f(x)$ be a quadratic polynomial with leading coefficient $1$ such that $f(0)=p, p \neq 0$ and $f(1)=\frac{1}{3}$. If the equations $f(x)=0$ and $f(f(f(f(x))))=0$ have a common real root,then $f(-3)$ is equal to $........$

If $\tan \alpha$ and $\tan \beta$ are the roots of the equation $x^2 + px + q = 0$ $(p \neq 0)$,then:

The minimum value of $f(x) = \frac{x^2-2x+3}{x^2-4x+7}$ is

Let $2 \sin^2 x + 3 \sin x - 2 > 0$ and $x^2 - x - 2 < 0$ ($x$ is measured in radians). Then $x$ lies in the interval

For $x \in R$,the number of real roots of the equation $3x^2 - 4|x^2 - 1| + x - 1 = 0$ is: